Least Common Multiple (LCM) of 43 and 169
The least common multiple (LCM) of 43 and 169 is 7267.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 43 and 169?
First, calculate the GCD of 43 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 169 = 0 remainder 43 |
| 2 | 169 ÷ 43 = 3 remainder 40 |
| 3 | 43 ÷ 40 = 1 remainder 3 |
| 4 | 40 ÷ 3 = 13 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 174 | 11832 |
| 96 and 91 | 8736 |
| 125 and 47 | 5875 |
| 129 and 101 | 13029 |
| 183 and 63 | 3843 |